6.2% of DVD players of a certain type are defective. Let the random variable X represent the number of defective DVD players among 200 randomly selected DVDs of this type. Suppose you wish to find the probability that X is less than 8.
(a) Does the random variable X have a binomial distribution or a Poisson distribution? Give reasons for your answer.
(b) If X has a binomial distribution, would it be reasonable to use the Poisson approximation to find P(X < 8)? Give reason(s) for your answer.
(c) Find P(X < 8).